Brilliance 77 · Fire 40 · Scintillation 66 · in our census, where the T73 scores 96 · 54 · 80 in YAG
How the Radiant Square Cut handles light in YAG, measured: brilliance 77, fire 40 and 18% leakage, set against the T73 in the same stone and against the same cut in diamond.
YAG has a refractive index of 1.833 and a dispersion of 0.028. Its critical angle, from the low end of that range, is 33.1°, so a round design needs a pavilion of at least 36.7° for head-on light to reflect off both sides of the pavilion and leave through the table. We trace it with one index, 1.833, the midpoint of the published range, and a fire spread of 0.024, 0.86 of the published dispersion. Every picture here is our Light Return tracer at 1.833, and every figure is from the same light census that scores the other gemstones; the 3D Gemstone Simulator shows the Radiant Square Cut in YAG live.
The Radiant Square Cut has 49 facets and a total depth of 72.8% of its width; its pavilion mains sit at 34.6°. In YAG, the census returns 77 of 100 for brilliance and 40 for fire, against 96 and 54 for the T73, our benchmark, in the same stone; the same Radiant Square Cut in diamond reads 72 and 62.
No figure ahead by our thresholds
Compared with the T73 Round Brilliant in YAG and with the Radiant Square Cut in diamond. A difference counts from 3 points (Brilliance, Fire, Tilt, Leakage), 5 (Scintillation, Symmetry), 4% (face-up size per carat) or 5% (weight); Tilt counts as a pro only for a stone within 5 points of the brilliance it is compared with. How we measure.
At a glance: the Radiant Square Cut in YAG (white) against the T73 Round Brilliant in YAG (dashed): solid white where it reaches further, hatched where it falls short. Each pro and con is explained, with pictures, below.
Against the T73 Round Brilliant in yag: ahead on 2, level on 1, behind on 5.
Against the T73 in YAG and the same cut in diamond, no figure of the Radiant Square Cut is ahead by the thresholds above. Its figures are in the wheel and the FAQ; YAG ranks every cut we score in YAG.
2.10 ct at 6.5 mm, against 1.62 ct for the same cut in diamond (+29%)
Weight follows specific gravity: 4.55 for YAG against 3.52 for diamond, so the same model at the same size weighs 2.10 ct here and 1.62 ct in diamond, 6.5 mm across. Nothing about the light changes with it.
Try it yourself: Weights in every gemstone on the Radiant Square Cut page
Fire 40 against 62 for the Radiant Square Cut in diamond: 22 points lower
Fire is the share of the returned light that splits into color at the exit facet: the census traces each exit again at the refractive index minus and plus the fire spread (0.024 in YAG) and counts a ray as fire when the two directions differ by more than 0.6°. The Radiant Square Cut reads 40 against 62 for the same cut in diamond. The figure is the census's; the 3D Gemstone Simulator renders YAG's fire live.
The fire figure is the census's, traced at the refractive index minus and plus the fire spread. See the fire in the 3D Gemstone Simulator: the Radiant Square Cut in YAG under the sunny-day lighting.
What helps: the DG-Elongated Hexagon reads 93 for fire in YAG, the best of the cuts we score there.
Brilliance 77 against 96 for the T73 Round Brilliant in YAG: 19 points lower
Brilliance is the share of the 3,200 census rays that enter the stone and come back out of the crown towards the viewer. In YAG, whose critical angle is 33.1°, the Radiant Square Cut returns 77 of 100 and the T73 96. The Radiant Square Cut's pavilion mains sit at 34.6°, the T73's at 40.8°. The maps below show where each stone's light returns from and where it leaks.
Radiant Square Cut in YAG · Brilliance 77
T73 Round Brilliant in YAG · Brilliance 96
What helps: the DG-M5 reads 97 for brilliance in YAG, the best of the cuts we score there.
Try it yourself: Open this Light Return map in the simulator
Scintillation 66 against 80 for the T73 Round Brilliant in YAG: 14 points lower
Scintillation follows the number of facets the stone shows: 100 × (1 − e^(−facets / 45)). The Radiant Square Cut has 49 facets and the T73 73, so 66 against 80. It depends on the geometry alone, so it is the same in every stone.
Radiant Square Cut · 49 facets · Scintillation 66
T73 Round Brilliant · 73 facets · Scintillation 80
What helps: the DG-Miliano reads 98 for scintillation in YAG, the best of the cuts we score there.
Try it yourself: Compare the Scintillation spoke in the Cut Performance Wheel
Against the T73 in YAG and the same cut in diamond, no figure of the Radiant Square Cut is ahead by our thresholds. The catch: it weighs more than in diamond, shows less fire than in diamond, returns less light than the T73 and has fewer facets to sparkle with.
If that catch matters more to you, the DG-Elongated Hexagon reads 93 for fire in YAG, the best of the cuts we score there.
Every figure on this page is from our light census, traced at one refractive index: a simulation of the geometry, not a grading report. The 3D files and cutting files below are the same Radiant Square Cut model we traced.
In our census the Radiant Square Cut returns 77 of 100 for brilliance and 40 for fire in YAG, against 96 and 54 for the T73 in the same stone. Against that round and against the same cut in diamond it has 0 pros and 4 cons by our thresholds; the summary above names them.
At least 36.7° for a round design: YAG's critical angle is 33.1°, from the low end of its refractive index range, and head-on light has to reflect off both sides of the pavilion and leave through the table. The Radiant Square Cut's pavilion mains sit at 34.6°.
At 6.5 mm across, 2.10 ct in YAG, against 1.62 ct for the same cut in diamond (+29%): YAG's specific gravity is 4.55, diamond's 3.52.
Yes: the 3D Gemstone Simulator renders it live, with YAG's own refractive index and dispersion. YAG is traced by the same light census as the other gemstones, with its refractive index and fire spread derived from published values, so its scores are on the same scale; the pictures here are our Light Return tracer, and the Cut Performance Wheel sets it against any other cut and stone.
The Radiant Square Cut as exact geometry: 49 planar facets, real-world scale, ready for CAD, rendering, printing and casting.
The Radiant Square Cut as a faceting design: 41 + 8 girdles = 49 facets, 96 index, 4-fold symmetry, ready for the machine.
Not sure the files open in your software? Get the cube free: the same six formats, for your email address, used only to send them (privacy).
Questions before you buy? Email us.
YAG: optical properties and the top ten cuts · The Radiant Square Cut: specifications, model and files